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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.13391 |
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| _version_ | 1866908306204786688 |
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| author | Granath, Andreas Åhag, Per Perälä, Antti Czyż, Rafał |
| author_facet | Granath, Andreas Åhag, Per Perälä, Antti Czyż, Rafał |
| contents | Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the inhomogeneous Cauchy-Riemann equations. Our method applies to domains conformally equivalent to a unit disk or an annulus, focusing on deriving explicit solutions for the displacement field rather than the stress tensor, which distinguishes it from most traditional approaches. We explore solutions for specific classical cases to demonstrate its efficacy, such as a cardioid domain, a ring domain with a shifted hole, and a gear-like structure. This work enhances the toolkit for researchers and practitioners tackling isotropic planar elastostatic challenges with a unified and flexible approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13391 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Explicit Solutions in Isotropic Planar Elastostatics Granath, Andreas Åhag, Per Perälä, Antti Czyż, Rafał Materials Science Complex Variables Primary 74B05, Secondary 30E25, 30C35, 31A10 Addressing the intricate challenges in plane elasticity, especially with non-vanishing traction and complex geometries, requires innovative methods. This paper offers a novel approach, drawing inspiration from the Neumann problem for the inhomogeneous Cauchy-Riemann equations. Our method applies to domains conformally equivalent to a unit disk or an annulus, focusing on deriving explicit solutions for the displacement field rather than the stress tensor, which distinguishes it from most traditional approaches. We explore solutions for specific classical cases to demonstrate its efficacy, such as a cardioid domain, a ring domain with a shifted hole, and a gear-like structure. This work enhances the toolkit for researchers and practitioners tackling isotropic planar elastostatic challenges with a unified and flexible approach. |
| title | Explicit Solutions in Isotropic Planar Elastostatics |
| topic | Materials Science Complex Variables Primary 74B05, Secondary 30E25, 30C35, 31A10 |
| url | https://arxiv.org/abs/2306.13391 |